Answer:
m = - 3
n = 2
Step-by-step explanation:
It can be solved using laws of exponents as given below:
[tex]5 {x}^{n} y(2 {x}^{4} {y}^{m} ) = \frac{10 {x}^{6} }{ {y}^{2} } \\ \\ (5 {x}^{n} .2 {x}^{4} )(y. {y}^{m} ) = 10 {x}^{6} {y}^{ - 2} \\ \\\cancel {10}\:\: {x}^{n + 4} . {y}^{m + 1} = \cancel {10}\:\: {x}^{6} {y}^{ - 2} \\ \\ {x}^{n + 4} . {y}^{m + 1} = {x}^{6} {y}^{ - 2} \\equating \: like \: terms \: on \: both \: sides \\ \\ {x}^{n + 4} = {x}^{6} \\ \\ \implies \: n + 4 = 6 \\ \\ n = 6 - 4 \\ \\ \huge \red{n = 2} \\ \\ {y}^{m + 1} = {y}^{ - 2} \\ \\ \implies \: m + 1 = - 2 \\ \\ m = - 2 - 1 \\ \\ \huge \purple{m = - 3}[/tex]
